Question

A charge of `40 C` passes through a circuit every `8 s`. If the circuit can generate `42 W` of power, what is the circuit's resistance?

Answer 1

`R = 1.68 Omega`

Explanation:

The current, `I`, is the charge passing through per unit time (`Q/C`).

So,

`I = frac{40"C"}{8"s"} = 5"A"`

The power arises from the fact that charges are moving over a potential difference.

`P=IV`

From Ohm's Law, we know that `V=IR` for an ideal resistance.

Therefore,

`P = I^2R`

`42"W" = (5"A")^2R`

`R = 1.68 Omega`

Answer 2

`1.68 Omega`

Explanation:

We'll need 2 formulae to answer this. namely:

`Q=It` and `P = I^2R`

Where Q is charge (40C), t is time (8s), P is power (42W), I is current and R is resistance.

Begin by using the first formula to obtain the current:

`I = Q/t = 40/8 = 5A`

Now use the second formula to get the resistance:

`R = P/I^2=42/5^2=42/25=1.68 Omega`